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Notes:
At the end of the main sequence, hydrogen fusion in the core stops. Hence, pressure stars to drop and the core shrinks. Hydrogen keeps being fused in shell around the core. As the core shrinks, the gravity in this shell increases, implying the pressure has to rise to carry the weight of the layers above. This causes the temperature to rise, which in turn leads to increases energy production. So much, indeed, that the outer layers expand.